Question

How do you solve and graph `|-2x + 4| > 6`?

Answer 1

`x<-1,` `x>5`

Refer to the explanation for the process and the graph.

Explanation:

Given:

`abs(-2x+4)>6`

Since `absa=+-a`, the inequality can be broken down into two: one positive and one negative.

`-2x+4>6color(white)(...)`and`color(white)(...)-(2x+4)>6`

Positive Inequality

`-2x+4>6`

Subtract `4` from both sides.

`-2x>6-4`

Simplify.

`-2x>2`

Divide both sides by `-2`. This will reverse the inequality.

`x<2/(-2)`

`x<-1`

Negative Inequality

`-(-2x+4)>6`

Simplify.

`2x-4>6`

Add `4` to both sides.

`2x>6+4`

Simplify.

`2x>10`

Divide both sides by `2`.

`x>5`

Solutions:

`x<-1`

`x>5`

Graph

The dots for `-1` and `5` are not filled in because they are not part of the inequality.